215 research outputs found
The dilute A model, the E mass spectrum and the tricritical Ising model
The exact perturbation approach is used to derive the (seven) elementary
correlation lengths and related mass gaps of the two-dimensional dilute A
lattice model in regime 2- from the Bethe ansatz solution. This model provides
a realisation of the integrable perturbation of the c=7/10
conformal field theory, which is known to describe the off-critical thermal
behaviour of the tricritical Ising model. The E masses predicted from
purely elastic scattering theory follow in the approach to criticality.
Universal amplitudes for the tricritical Ising model are calculated.Comment: 24 pages, LaTeX, submitted to Journal of Mathematical Physics. One
paragraph added and some minor typos correcte
Magnetic Correlation Length and Universal Amplitude of the Lattice E_8 Ising Model
The perturbation approach is used to derive the exact correlation length
of the dilute A_L lattice models in regimes 1 and 2 for L odd. In regime
2 the A_3 model is the E_8 lattice realisation of the two-dimensional Ising
model in a magnetic field h at T=T_c. When combined with the singular part f_s
of the free energy the result for the A_3 model gives the universal amplitude
as in precise agreement with the result
obtained by Delfino and Mussardo via the form-factor bootstrap approach.Comment: 7 pages, Late
Bailey flows and Bose-Fermi identities for the conformal coset models
We use the recently established higher-level Bailey lemma and Bose-Fermi
polynomial identities for the minimal models to demonstrate the
existence of a Bailey flow from to the coset models
where is a
positive integer and is fractional, and to obtain Bose-Fermi identities
for these models. The fermionic side of these identities is expressed in terms
of the fractional-level Cartan matrix introduced in the study of .
Relations between Bailey and renormalization group flow are discussed.Comment: 28 pages, AMS-Latex, two references adde
The perturbations and of the minimal models and the trinomial analogue of Bailey's lemma
We derive the fermionic polynomial generalizations of the characters of the
integrable perturbations and of the general minimal
conformal field theory by use of the recently discovered trinomial
analogue of Bailey's lemma. For perturbations results are given
for all models with and for perturbations results for all
models with are obtained. For the
perturbation of the unitary case we use the incidence matrix
obtained from these character polynomials to conjecture a set of TBA equations.
We also find that for with and for
satisfying there are usually several different fermionic polynomials
which lead to the identical bosonic polynomial. We interpret this to mean that
in these cases the specification of the perturbing field is not sufficient to
define the theory and that an independent statement of the choice of the proper
vacuum must be made.Comment: 34 pages, 15 figures, harvmac. References added and the TBA
conjecture refine
Bounded Littlewood identities
We describe a method, based on the theory of Macdonald-Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald's partial fraction technique and results in the first examples of bounded Littlewood identities for Macdonald polynomials. These identities, which take the form of decomposition formulas for Macdonald polynomials of type (R,S) in terms Macdonald polynomials of type A, are q,t-analogues of known branching formulas for characters of the symplectic, orthogonal and special orthogonal groups, important in the theory of plane partitions.
As applications of our results we obtain combinatorial formulas for characters of affine Lie algebras, Rogers-Ramanujan identities for such algebras complementing recent results of Griffin et al., and transformation formulas for Kaneko-Macdonald-type hypergeometric series
Dilute Birman--Wenzl--Murakami Algebra and models
A ``dilute'' generalisation of the Birman--Wenzl--Murakami algebra is
considered. It can be ``Baxterised'' to a solution of the Yang--Baxter algebra.
The vertex models are examples of corresponding solvable
lattice models and can be regarded as the dilute version of the
vertex models.Comment: 11 page
An exact universal amplitude ratio for percolation
The universal amplitude ratio for percolation in two
dimensions is determined exactly using results for the dilute A model in regime
1, by way of a relationship with the q-state Potts model for q<4.Comment: 5 pages, LaTeX, submitted to J. Phys. A. One paragraph rewritten to
correct error
Review of Ramazani, R.K. (2013) Independence without freedom: Iran's foreign policy
Middle Eastern Studie
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